14 research outputs found
On the existence of a compact generator on the derived category of a noetherian formal scheme
In this paper, we prove that for a noetherian formal scheme X, its derived
category of sheaves of modules with quasi-coherent torsion homologies D_qct(X)
is generated by a single compact object. In an appendix we prove that the
category of compact objects in D_qct(X) is skeletally small.Comment: 13 page
Perverse coherent t-structures through torsion theories
Bezrukavnikov (later together with Arinkin) recovered the work of Deligne
defining perverse -structures for the derived category of coherent sheaves
on a projective variety. In this text we prove that these -structures can be
obtained through tilting torsion theories as in the work of Happel, Reiten and
Smal\o. This approach proves to be slightly more general as it allows us to
define, in the quasi-coherent setting, similar perverse -structures for
certain noncommutative projective planes.Comment: New revised version with important correction
Approximations and adjoints in homotopy categories
Krause H. Approximations and adjoints in homotopy categories. Mathematische Annalen. 2012;353(3):765-781.We provide a criterion for the existence of right approximations in cocomplete additive categories; it is a straightforward generalisation of a result due to El Bashir. This criterion is used to construct adjoint functors in homotopy categories. Applications include the study of (pure) derived categories. For instance, it is shown that the pure derived category of any module category is compactly generated